Problem: Solve for $x$ and $y$ using elimination. ${-2x-3y = -19}$ ${5x+3y = 34}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $3x = 15$ $\dfrac{3x}{{3}} = \dfrac{15}{{3}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-2x-3y = -19}\thinspace$ to find $y$ ${-2}{(5)}{ - 3y = -19}$ $-10-3y = -19$ $-10{+10} - 3y = -19{+10}$ $-3y = -9$ $\dfrac{-3y}{{-3}} = \dfrac{-9}{{-3}}$ ${y = 3}$ You can also plug ${x = 5}$ into $\thinspace {5x+3y = 34}\thinspace$ and get the same answer for $y$ : ${5}{(5)}{ + 3y = 34}$ ${y = 3}$